Mathematics: A chemist measures the temperature in degrees Fahrenheit of a chemical compound every hour. The temperatures approximate a geometric sequence where an is the temperature at a given hour, and n is the hour. At hour 4, the temperature is 70 °F and at hour 6 the temperature is 80 °F. Pls include the value of A1 A4 A6 and r thanks

A chemist measures the temperature in degrees Fahrenheit

Ответ:

ventalexander8406

19.01.2022

$A_{1}=57^{0}F; A_{4}=70^{0}F; A_{6}=80^{0}F; r=1.07$

Step-by-step explanation:

The formula for calculating the nth term of a Geometric Sequence is given as: $A_{n}=ar^{n-1}$ where n is the number of term, r=common ratio and a=first term.

At hour 4, the temperature is $70^{0}$ F

$A_{4}=70, n=4\\70=ar^{4-1}=ar^{3}$ .......(i)

At hour 6 the temperature is 80°F.

$A_{6}=80, n=6\\80=ar^{6-1}=ar^{5}$ ......(ii)

Solving (i) and (ii) simultaneously

$\frac{80}{70}=\frac{ar^{5}}{ar^{3}} \\x^{2} r^{2} =\frac{8}{7}\\r=\sqrt{\frac{8}{7}}=1.07$

Plugging r into equation (i), we could use (ii) as well,

$70=ar^{3}$

$70=a(\sqrt{\frac{8}{7}})^{3}$

$a=\frac{70}{\sqrt{(\frac{8}{7}})^{3}}$

$a=\frac{245}{8}\sqrt{\frac{7}{2} }$ =57.29

Therefore:

$A_{1}=57^{0}F; A_{4}=70^{0}F; A_{6}=80^{0}F; r=1.07$

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